Question

current attempt in progress
in the following right triangle, if $a = 12$ and $c = 13$, find $b$.
enter the exact answer.
$b=$

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. We need to solve for $b$, so $b^{2}=c^{2}-a^{2}$.

Step2: Substitute given values

Given $a = 12$ and $c = 13$, then $b^{2}=13^{2}-12^{2}=169 - 144=25$.

Step3: Find the value of $b$

Take the square root of both sides. Since $b$ represents a side - length (a non - negative quantity), $b=\sqrt{25}=5$.

Answer:

$5$